Modeling the mechanosensitivity of fast-crawling cells on cyclically stretched substrates

Abstract

The mechanosensitivity of cells, which determines how they are able to respond to mechanical signals received from their environment, is crucial for the functioning of all biological systems. In experiments, cells placed on cyclically stretched substrates have been shown to reorient in a direction that depends not only on the type of cell, but also on the mechanical properties of the substrate, and the amplitude and rate of stretching. However, the underlying biochemical and mechanical mechanisms responsible for this realignment are still not completely understood. In this study, we introduce a computational model for fast crawling on cyclically stretched substrates that accounts for the sub-cellular processes responsible for the cell shape and motility, as well as the coupling to the substrate through the focal adhesion sites. In particular, we focus on the role of the focal adhesion dynamics, and show that the reorientation under cyclic stretching is strongly dependent on the frequency, as has been observed experimentally. Furthermore, we show that an asymmetry during the loading and unloading phases of the stretching, whether coming from the response of the cell itself, or from the stretching protocol, can be used to selectively align the cells in either the parallel or perpendicular directions. *

Rotating lamellipodium waves in polarizing cells

“…It is then straightforward to show, using Eqs. 2, (31), and (33), that Eq. 35is satisfied if the amplitudes R 1 and R 2 follow the coupled amplitude equations given by Eqs.…”

“…Using the recently developed phase field approach, see refs. [24][25][26][27][28][29][30][31][32][33][34][35][36] for recent comprehensive reviews, we demonstrate the occurrence of protrusion waves and analyze their formation and competition within a minimal physical model. Our study revealed that the onset and competition of rotating lamellipodium waves can be captured in the framework of a model incorporating cell shape dynamics, actin polymerization, substrate deformation, and adhesion.…”

Spontaneous spatiotemporal ordering of shape oscillations enhances cell migration

“…Through tuning the duration of the internal cycle of cells it becomes possible to either enhance the migration of cells, or, to the contrary, diminish the migration of non-desirable (malignant) cells. Influencing the cycle duration might be accomplished through manipulating the substrate, e.g., periodic stretching of the substrate is able to reorient solitary crawling cells (28,(66)(67)(68)(69)(70)(71). A first step will be to verify our results in experiments that track cells individually and discriminate between expanding and contracting cells, which allows to compute the correlations C(x , y ) and S(x , y ) introduced here.…”

“…Several physics-based representations of cells have been proposed in the literature (14,15). Most prominently, deformable active particles (16)(17)(18)(19)(20), vertex (21,22) or Voronoi models (23,24), phase field models (25)(26)(27)(28), active gel models (29,30), and subcellular element models (31)(32)(33)(34)(35) have been investigated. Among these, subcellular element models offer the advantage of naturally taking into account the internal structure and internal forces, as well as shape deformations within a single cell.…”

Tools for computational analysis of moving boundary problems in cellular mechanobiology

“…Originally developed to solve physical problems of phase separation that have well defined energy functionals (Cahn & Hilliard, 1958), it has been adapted to simulate systems with moving boundaries. In particular, numerous applications have appeared which rely of PFM for simulating cell migration (Alonso, Stange, & Beta, 2018; Bresler, Palmieri, & Grant, 2019; Camley et al, 2014; Cao et al, 2019; Gomez, Bures, & Moure, 2019; Kulawiak, Camley, & Rappel, 2016; Löber, Ziebert, & Aranson, 2015; Molina & Yamamoto, 2019; Moure & Gomez, 2018; Moure & Gomez, 2020a, 2020b; Shao et al, 2010; Shao, Levine, & Rappel, 2012; Tao et al, 2020) and, to a lesser degree, cytokinesis (Zhao & Wang, 2016a, 2016b).…”